# Sale Prices: Fifty Seven Point Five Percent Off on Streets of Canterbury!

Whilst wandering through the streets of Canterbury this sign caught my eye. With the mathematics department’s favourite coffee shop in the back-ground, the sign promises a further drop of prices for outdoor enthusiasts.

‘Half price’ and ‘15%’ are both eye catching figures which are immediately understandable to the shopper, but the sign promises something else.

Will anyone think this is a ‘65% off’ sale and that bargains can be picked up for 35% of their recommended retail price(RRP)?

In fact a 15% reduction applied to a 50% sale is compound percentage problem best dealt with by percentage multipliers:

$0.5 \times 0.85 =0.425$

that is, half price with a further 15% applied amounts to a reduction of 57.5% with shoppers paying 42.5% of the RRP rather than 35%. Are the marketeers messing with our heads?

Perhaps nicer for the maths teachers in the coffee shop to see calculate in fractioons without electronic assistance:

$\dfrac{50}{100} \times \dfrac{85}{100}= \dfrac{1}{2} \times \dfrac{17}{20}=\dfrac{17}{40}$

Much nicer perhaps, but a ‘$\frac{23}{40}$ off’ sale doesn’t have the same ring about it I suppose.